How can active learning be used in the case of complex models that require a lot of data?
As I found this case backs to the sequence labeling. Sequence labeling has some classic solution such as conditional random fields (CRFs) and hidden Markov model (HMM). Also, have some solution in Active learning (AL) which use from algorihtms such as struct SVM ($\text{SVM}^{\text{strcut}}$) like this paper.

Also, some NLP solutions in active learning could help to solve these kind of problems such as this paper which is about active learning in named entity recognition (NER).

Besides, the combination of active learning with Deep networks such as CNN happens. For example, this paper explains more about the idea.